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For the matrix A=[{:(1,1,1),(1,2,-3),(2,...

For the matrix `A=[{:(1,1,1),(1,2,-3),(2,-1,3):}]` Show that `A^3-6A^2+5A+11I=O`. Hence find `A^(-1)`

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The correct Answer is:
`thereforeA^(-1)=1/(11)[{:(-3,4,5),(9,-1,-4),(5,-3,-1):}]`
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For matrix A=[{:(1,1,1),(1,2,-3),(2,-1,3):}] . Prove that , A^(3)-6A^(2)+5A+11I=0 . Hence find A^(-1) using it .

If A=[{:(3,1),(-1,2):}] show that A^2-5A+7I=O . Hence find A^(-1)

For the matrix A=[{:(1,2,2),(2,1,2),(2,2,1):}] . Show that A^2-4A-5I=0 Hence find A^(-1)

If A=[{:(1,2,1),(2,1,3),(1,1,0):}] then prove that A^3-2A^2-7A-4I_3=0 . Hence find A^(-1)

If A=[{:(2,-1,1),(-1,2,-1),(1,-1,2):}] Verify the result A^3-6A^2+9A-4I=O and hence find A^(-1)

If A=[{:(1,2,3),(3,-2,1),(4,2,1):}] , then show that A^(3)-23A-40I=O .

If A=[{:(1,0,2),(0,2,1),(2,0,3):}] then , prove that A^(3)-6A^(2)+7A+2I=O .

For the matrix A=[{:(2,3),(1,2):}] , show that A^2-4A+I_2=0 . Hence, find A^(-1)

If A=[{:(3,1),(-1,2):}] , show that A^(2)-5A+7I=O .

Find A^(-1)" if "A=[{:(0,1,1),(1,0,1),(1,1,0):}] and show that A^(-1)=(A^2-3I)/2

KUMAR PRAKASHAN-DETERMINANTS -Exercise 4.5
  1. Find adjoint of each of the matrices in Exercises 1 and 2 [{:(1,2),(...

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  2. Find adjoint of each of the matrices in Exercises 1 and 2 [{:(1,-1,2...

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  3. Verify A(adjA)=(adjA) A=|A| I in following examples (3) and (4) [{:(...

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  4. Verify A(adjA)=(adjA) A=|A| I in following examples (3) and (4) [{:...

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  5. Find the inverse of each of the matrices (if it exists ) {:[( 2,-2),...

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  6. Find the inverse of each of the matrices (if it exists ) {:[( 2,-2),...

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  7. Find the inverse of each of the following matrices (if it exits) given...

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  8. Find the inverse of each of the following matrices (if it exits) given...

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  9. Find the inverse of each of the following matrices (if it exits) given...

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  10. Find the inverse of each of the following matrices (if it exits) given...

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  11. Find the inverse of each of the following matrices (if it exits) given...

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  12. Let A=[{:(3,7),(2,5):}] and B=[{:(6,8),(7,9):}] Verify that (AB)^(-1)=...

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  13. If A=[{:(3,1),(-1,2):}] show that A^2-5A+7I=O. Hence find A^(-1)

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  14. For the matrix A=[{:(3,2),(1,1):}] , find the numbers a and b such tha...

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  15. For the matrix A=[{:(1,1,1),(1,2,-3),(2,-1,3):}] Show that A^3-6A^2+5A...

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  16. If A=[{:(2,-1,1),(-1,2,-1),(1,-1,2):}] Verify the result A^3-6A^2+9A-4...

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  17. Let A be a nonsingular square matrix of order 3xx3.Then |adj A| is equ...

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  18. If A is an invertible matrix of order 2, then det (A^(-1)) is equal to...

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